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Positive area and inaccessible fixed points for hedgehogs | | Kingshook Biswas
; | | Date: |
21 Oct 2010 | | Abstract: | Let f be a germ of holomorphic diffeomorphism with an irra- tionally
indifferent fixed point at the origin in C (i.e. f(0) = 0, f’(0) = e 2pi i
alpha, alpha in R - Q). Perez-Marco showed the existence of a unique family of
nontrivial invariant full continua containing the fixed point called Siegel
compacta. When f is non-linearizable (i.e. not holomorphically conjugate to the
rigid rotation R_{alpha}(z) = e 2pi i z) the invariant compacts obtained are
called hedgehogs. Perez-Marco developed techniques for the construction of
examples of non-linearizable germs; these were used by the author to construct
hedge- hogs of Hausdorff dimension one, and adapted by Cheritat to construct
Siegel disks with pseudo-circle boundaries. We use these techniques to
construct hedgehogs of positive area and hedgehogs with inaccessible fixed
points. | | Source: | arXiv, 1010.4496 | | Services: | Forum | Review | PDF | Favorites | |
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